Rig won't change Model
You parented the rig to the body.

But you should be parenting the body to the rig, so you select the body then hold SHIFT and then select the rig (in object mode) then press CTRL+P then choose with automatic weights. After that try moving the bones in pose mode.

Don't forget to let me know if that works or not.

You might have to remove the first parent to do this.

Good luck.